1. Technical Field
The invention relates to fully recurrent analog neural networks and in particular to apparatus and methods of training such networks by continuous updating of synapse weights and neuron temperatures.
2. Background Art
A problem that has remained consistently at the forefront of neural network research for the past several years, concerns the scalability of both neural networks architectures and their associated learning algorithms. Novel ideas for fast learning algorithms have surfaced in the literature, and include such formalisms as networks with non-Lipschitzian dynamics; terminal attractors; and locally-tuned processing units. There have also been significant developments in the area of dynamically reconfigurable neural network topologies for optimal use of processing assets. These include the resource allocating neural network (RANN) and the cascade correlation neural network (CCNN). However, the concern still remains that these approaches are geared toward `small` problems that can be relatively easily implemented and trained in software within finite time on sequential digital computers. However, complex network architectures, which can model more realistic problems, often require specialized parallel hardware solutions as they prove to be otherwise frequently intractable computationally. Although such parallel hardware solutions are just beginning to emerge commercially, the problem of fast parallel on-chip or off-chip learning is still an issue. The fundamental problem in learning, therefore, is to further develop, refine and speed-up present learning algorithms which are capable of either extracting or memorizing the functional relationship linking the input-output data pairs of observations in a more rapid fashion. Of course the desire is to consequently use this information to predict the correct response to novel input patterns in real time.
In this specification, our initial focus is to develop the necessary mathematical formalism for a new connectionist learning architecture called the Adaptive Neuron Model (ANM) which has been designed to rapidly learn arbitrary, complex, nonlinear transformations from example. As the name of the model implies, the architecture allows both the synaptic and neuronal parameters to adapt. Training statistics indicate a considerable gain in training time is achievable. This model has been applied to a broad class of problems and has been shown to achieve functional synthesis on the training data. Of particular relevance to applications of the ANM model, is the class of problems commonly known as inverse mapping problems. These inverse problems are typically nonlinear, and are usually characterized by their one-to-many mapping operation. In other words, the specification of a goal does not uniquely determine the action that must be carried out to meet the task at hand. Such systems are said to be redundant or degenerate. This means that there can exist numerous if not an infinite number of distinct solutions for the system variables, whilst at the same time being entirely consistent with the desired task at hand.
Specifically, a problem that fits directly into this mold and has received much attention from the neural network community is that of the inverse kinematic problem for a robotic manipulator with excess degrees of freedom. It should be observed that biological systems handle such ill-defined or ill-structured problems such as sensorimotor control with remarkable ease and flexibility and reveal a spontaneous emergent ability that enables them to adapt their structure and function. This provides the motivation for recourse to biologically inspired paradigms for such problems. The inverse kinematic problem has been selected to benchmark the performance of the ANM learning algorithm. The inventor has previously addressed this same problem from the perspective of a feed-forward network employing the backpropagation algorithm, as disclosed in U.S. patent application Ser. No. 07/473,024 filed Jan. 31, 1990 by the present inventor and entitled "Neural Network with Dynamically Adaptable Neurons." The use of connectionist architectures is not limited to the inverse kinematic problem only. In fact neural networks have been used for (a) unsupervised adaptive visual-motor coordination of a multijoint arm where the system can learn sensory-motor control from experience, (b) dynamic control of manipulators based on the CMAC approach of Albus, and (c) the neural learning of the mapping transformation between desired trajectory formation and the corresponding actuator movement.
In selecting a neural network architecture, thought must also be given to the method for lifting the degeneracy problem present in these inverse mappings. Two distinct ways exist for achieving this. It can be accomplished with the introduction of constraints embedded a priori within the training set. This is the method which we pursue in this specification when forming the training set for the 3-link robotic manipulator. It may also be accomplished with the introduction of a penalty term within the energy function. The neural network is then trained to provide a solution that optimizes the penalty function p(x) that meets the specified constraints.
In order to illustrate these points, we borrow an example from linear algebra. Consider the problem of an under constrained system of equations of the unknown variable x of the form Ax=b. Here, b is a constant vector quantity, and A is the matrix of constant coefficients. For an under-constrained system of equations, there is no possible way for determining a unique solution to x and in fact there exist an infinite number of solutions for it. Unique solutions can only be obtained by the introduction of an adequate number of constraints equation in the variable x so as to properly constrain the system.
In the last section of this specification, we report on an electronic implementation of the resulting neural network architecture that was put together from custom analog `building block` neural network chips developed at the Jet Propulsion Laboratory. This electronic neuroprocessor has been interfaced with a commercially available Heathkit five degree of freedom robotic arm. In this example, the arm was constrained to motion in the vertical plane using three degrees of freedom out of a total of five available degrees. The electronic neuroprocessor was shown to be capable of guiding the manipulator along arbitrary trajectories in real-time.